Let f = fraction, M = mass, V = volume

subscripts: a=air, w=water, s=solid, t=total, f=fluid
 

Hillel’s notation differs slightly from that commonly found in the literature.  I'll use Hillel notation for this course, but you should know that::

    Porosity:  Hillel’s f = more usually given as φ

    Degree of saturation:  Hillel’s s = more usually given as S (saturation) or Θ

    Voil ratio:  Hillel’s e = more usually given as ε
 

Note that M_a is generally ignored, and we frequently assume ρ_w = 1 gm/cm³ = 1000 kg m³.
 

Definitions:

Total volume:        V_t = V_f + V_s = V_a + V_w + V_s
 

Total mass:        M_t = M_f + M_s = M_a + M_w + M_s
 

wet bulk density:        ρ_t = (M_s + M_w) / (V_s + V_a + V_w)
 

dry bulk density:        ρ_b= M_s / (V_s + V_a + V_w)
 

porosity:            f = V_f / V_t
 

air-filled porosity:        f_a = V_a / V_t
 

mass wetness:        w = M_w / M_s
 

volume wetness:        θ = V_w / V_t
 
 

Conversions:

porosity and void ratio:

            e = f / (1 - f)

            f = e / (1 + e)

volume wetness and mass wetness:

            θ = w ρ_b / ρ_w

            W = θ ρ_w / ρ_b

volume wetness and degree of saturation:

            θ = s f

            s = θ / f

porosity and bulk density:

            f = 1 - ρ_b / ρ_s

            ρ_b = (1 - f) ρ_s